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Binomial Markov Chain model

Source: R/model_doc.R
BinMC.Rd

This is a state-space model defined by a Binomial measurement error and a latent Markov Chain. For more details see the BinRW vignette.

Arguments

max_score

Maximum value that the score can take

prior

Named list of the model's priors. If NULL, uses the default prior for the model (see default_prior()).

Details

Details of the model are available in the paper.

Parameters

Population parameters:

  • sigma: Standard deviation of the evolution of ss1

  • mu_logit_p10: Population logit mean of p10

  • sigma_logit_p10: Population logit standard deviation of p10

Patient-dependent parameters:

  • p10: Probability of transitioning from state 1 to state 0

  • logit_p10: logit of p10

  • logit_tss1_0: Initial condition of the logit(ss1 * (1 + p10))

Observation-dependent (patient- and time-dependent) parameters:

  • p01: Probability of transitioning from state 0 to state 1

  • lambda: Mobility of the Markov Chain (eigenvalue of the transition matrix)

  • ss1: Steady state probability of state 1

  • y_lat: Latent score (probability)

See list_parameters(model = "BinMC") for more details.

Priors

The priors are passed as a named list with elements sigma, mu_logit_p10 and sigma_logit_p10 specifying priors for the corresponding parameters. Each element of the list should be a vector of length 2, containing values for x1 and x2, x2 > 0, such as:

  • sigma ~ normal+(x1, x2)

  • mu_logit_p10 ~ normal(x1, x2)

  • sigma_logit_p10 ~ normal+(x1, x2)

  • logit_tss1_0 ~ normal(x1, x2)

NB: For sigma and sigma_logit_p10, usually x1=0 to define a half-normal distribution since the parameter is constrained to be positive.

Default priors

  • The default prior for sigma translates to an odd ratio increment of at most 5 (~ 2 * upper bound of prior).

  • The default priors for mu_logit_p10 and sigma_logit_p10 translate to an approximately uniform prior on p10.

  • The prior for the initial condition of ss1 is hard coded and a function of p10.

Examples

EczemaModel("BinMC", max_score = 100)
#> BinMC model (discrete)
#> max_score = 100 
#> Prior: 
#> - sigma ~ normal+(0,0.4)
#> - mu_logit_p10 ~ normal(0,1)
#> - sigma_logit_p10 ~ normal+(0,1.5)
#> - logit_tss1_0 ~ normal(-1,1)